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| Cable Defect Localization Method Based on Short-Time Fractional Fourier Transform and Time-Frequency Domain Reflectometry |
| Rao Xianjie1, Xu Zhonglin1, Ding Yuqin1, Hu Xiaoyu1, Zhou Kai2 |
1. Chengdu Power Supply Company State Grid Sichuan Power Supply Company Chengdu 610041 China;
2. College of Electrical Engineering Sichuan University Chengdu 610065 China |
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Abstract The time-frequency domain reflectometry (TFDR) method is widely used to detect and locate cable defects. However, traditional TFDR methods have problems such as low time-frequency resolution and severe cross-term interference, which make it difficult to accurately locate weak cable defects. To address these issues, this paper proposes a cable defect localization method based on short-time fractional Fourier transform (STFRFT) and TFDR. The STFRFT is used to obtain the high-resolution time-frequency distribution of the incident signal and the reflected signal, which can maintain the compact support of the signal in the time-frequency domain and eliminate cross-term interference.
Firstly, in the distributed parameter model of the power cable, the incident signal of TFDR is the Gaussian envelope linear frequency modulation signal, which can produce the reflected signal with the same time-frequency domain characteristic. So both the incident signal and the reflected signal have compact support in the time-frequency domain. Secondly, the STFRFT has a high resolution for non-stationary signals such as the linear frequency modulation signal, therefore the frequency variation coefficient of the TFDR reference signal is used to determine the rotation angle of STFRFT, which can obtain a high-resolution time-frequency distribution of the incident signal and the reflected signal. Finally, the time-frequency cross-correlation function is established as the cable defect localization curve, and the local peak of the curve shows the location of the cable defect.
The time-frequency distributions of multi-component reference signals show that, the quadratic transformation of the Wigner-Ville distribution (WVD) causes serious cross-term interference, which significantly affects the authenticity of the time-frequency distribution. The Fourier transform of synchronous squeezing transformation (SST) makes it difficult to focus the frequency domain energy of the linear frequency modulation signal, leading to the signal energy dispersion in the time-frequency distribution. The time-varying time-frequency resolution in the S-transform causes signal energy distortion in the time-frequency distribution, which weakens the compact support of the signal in the time-frequency domain. Because the STFRFT can effectively focus the signal energy in the time-frequency domain, the proposed method can accurately obtain a high-resolution time-frequency distribution of the incident signal and the reflected signal, and it can eliminate cross-term interference.
In this paper, the 500 m 10 kV power cable simulation model is established. The defect is located at 300 m, while the defect length is 1 m. Since the defect can change the characteristic impedance of the local area, this paper sets the characteristic impedance of the simulated defect area to 1.05 times that of the normal area. The local peak of the proposed defect localization curve can accurately locate the cable defect with an error of only 0.79 m. In addition, the peak value of the defect is 0.98, which approaches the maximum value 1 of the curve. Meanwhile, there are no false local peaks in the proposed defect localization curve.
In the measurement process, the experimental subject is a 105 m 10 kV XLPE power cable, which has a local corrosion defect caused by water. To suppress the cross-term interference, orthogonal matching pursuit and pseudo Wigner-Ville distribution (OMP-PWVD) need to sacrifice the time-frequency resolution of the reflected signal, while smoothed pseudo Wigner-Ville distribution (SPWVD) need to sacrifice the time-frequency energy of the reflected signal. As a result, the traditional OMP-PWVD and SPWVD make it difficult to locate the local corrosion defect in the power cable. As same as the simulation results, the proposed defect localization curve can accurately locate the defect, in which the positioning error is only 0.99 m.
The conclusions of this article are summarized as follows: (1) In STFRFT, the signal can be converted to the fractional domain by rotation angle θ. Based on the time-frequency characteristics of the TFDR reference signal, the θ is set to arccot[-b/(2π)], which can effectively focus the signal energy and improve signal resolution in the time-frequency domain. (2) Compared with traditional methods, the time-frequency distribution of the STFRFT can keep the compact support of signal in the time-frequency domain and eliminate cross-term interference. (3) The defect localization results of a 500 m cable model and a 105 m 10 kV power cable show that the proposed method can sensitively locate cable defects with a high positioning accuracy. Compared with traditional OMP-PWVD and SPWVD, the method proposed in this paper has a better defect localization result.
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Received: 19 February 2024
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2025, Vol. 40 
